This paper presents a full-wave analysis of cross polarization and transmission loss effects caused by a dielectric hemi-spherical radome and rainfall. The radome covered by a rain-water layer is centre-placed on an aperture on the ground plane and excited by the Dominant TE11 circular waveguide. The dyadic Green's function (DGF) technique that serves as a full-wave analysis is applied in the analysis, instead of the conventional analytical techniques. Numerical computations with excellent accuracy and fast convergence are carried out by using Mathematica package to demonstrate the effects of the radome with a rain-water layer on the far-field power pattern, cross polarization and total transmission loss. It is hown that the antenna radiation performance such a antenna pattern, transmission loss, and cross polarization becomes severely affected when the thickness of the dielectric radome is selected improperly, and is further degraded when rain water accumulates on the dielectric radome.